# Properties

 Label 1122g Number of curves $2$ Conductor $1122$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("g1")

sage: E.isogeny_class()

## Elliptic curves in class 1122g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1122.g2 1122g1 $$[1, 1, 1, -411787, -97932871]$$ $$7722211175253055152433/340131399900069888$$ $$340131399900069888$$ $$$$ $$16224$$ $$2.1271$$ $$\Gamma_0(N)$$-optimal
1122.g1 1122g2 $$[1, 1, 1, -1108107, 319580601]$$ $$150476552140919246594353/42832838728685592576$$ $$42832838728685592576$$ $$$$ $$32448$$ $$2.4737$$

## Rank

sage: E.rank()

The elliptic curves in class 1122g have rank $$0$$.

## Complex multiplication

The elliptic curves in class 1122g do not have complex multiplication.

## Modular form1122.2.a.g

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} + q^{4} + 2q^{5} - q^{6} - 2q^{7} + q^{8} + q^{9} + 2q^{10} + q^{11} - q^{12} + 4q^{13} - 2q^{14} - 2q^{15} + q^{16} + q^{17} + q^{18} - 2q^{19} + O(q^{20})$$ ## Isogeny matrix

sage: E.isogeny_class().matrix()

The $$i,j$$ entry is the smallest degree of a cyclic isogeny between the $$i$$-th and $$j$$-th curve in the isogeny class, in the Cremona numbering.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with Cremona labels. 